Comparing first-passage times for semi-Markov skip-free processes

For two semi-Markov positive skip-free processes on conditions are given such that the first-passage times from the reflecting state 0 to a preassigned threshold are ordered according to Laplace and to increasing linear orderings. A comparison of first-passage times is performed via the new notion of [`]dual weak likelihood ratio ordering'. An application to life times of devices subject to shocks and repairs is finally provided.